On operator growth and emergent Poincar\'e symmetries
- URL: http://arxiv.org/abs/2002.03865v1
- Date: Mon, 10 Feb 2020 15:29:50 GMT
- Title: On operator growth and emergent Poincar\'e symmetries
- Authors: Javier M. Magan and Joan Simon
- Abstract summary: We consider operator growth for generic large-N gauge theories at finite temperature.
The algebra of these modes allows for a simple analysis of the operators with whom the initial operator mixes over time.
We show all these approaches have a natural formulation in terms of the Gelfand-Naimark-Segal (GNS) construction.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider operator growth for generic large-N gauge theories at finite
temperature. Our analysis is performed in terms of Fourier modes, which do not
mix with other operators as time evolves, and whose correlation functions are
determined by their two-point functions alone, at leading order in the large-N
limit. The algebra of these modes allows for a simple analysis of the operators
with whom the initial operator mixes over time, and guarantees the existence of
boundary CFT operators closing the bulk Poincar\'e algebra, describing the
experience of infalling observers. We discuss several existing approaches to
operator growth, such as number operators, proper energies, the many-body
recursion method, quantum circuit complexity, and comment on its relation to
classical chaos in black hole dynamics. The analysis evades the bulk vs
boundary dichotomy and shows that all such approaches are the same at both
sides of the holographic duality, a statement that simply rests on the equality
between operator evolution itself. In the way, we show all these approaches
have a natural formulation in terms of the Gelfand-Naimark-Segal (GNS)
construction, which maps operator evolution to a more conventional quantum
state evolution, and provides an extension of the notion of operator growth to
QFT.
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